Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

1:39 minutes

Problem 41a

Textbook Question

Simplify each exponential expression in Exercises 23–64. (−4/x)^3

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponential Expressions

Exponential expressions involve a base raised to a power, indicating how many times the base is multiplied by itself. In the expression (−4/x)^3, the base is (−4/x) and the exponent is 3, meaning the base will be multiplied by itself three times. Understanding how to manipulate these expressions is crucial for simplification.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, x^(-n) is equivalent to 1/(x^n). In the expression (−4/x)^3, recognizing that x in the denominator can be treated with a negative exponent will aid in simplifying the expression correctly.

Distributive Property

The distributive property allows us to multiply a single term by each term within a parenthesis. When simplifying (−4/x)^3, applying the distributive property helps in expanding the expression to separate the base and the exponent, leading to clearer simplification steps. This property is essential for handling expressions with multiple components.